Problem: Simplify the following expression: $ p = \dfrac{-3}{4} + \dfrac{-1}{y + 9} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{y + 9}{y + 9}$ $ \dfrac{-3}{4} \times \dfrac{y + 9}{y + 9} = \dfrac{-3y - 27}{4y + 36} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{-1}{y + 9} \times \dfrac{4}{4} = \dfrac{-4}{4y + 36} $ Therefore $ p = \dfrac{-3y - 27}{4y + 36} + \dfrac{-4}{4y + 36} $ Now the expressions have the same denominator we can simply add the numerators: $p = \dfrac{-3y - 27 - 4}{4y + 36} $ $p = \dfrac{-3y - 31}{4y + 36}$